Discrepancy principle for statistical inverse problems with application to conjugate gradient iteration
- The authors discuss the use of the discrepancy principle for statistical inverse problems, when the underlying operator is of trace class. Under this assumption the discrepancy principle is well defined, however a plain use of it may occasionally fail and it will yield sub-optimal rates. Therefore, a modification of the discrepancy is introduced, which corrects both of the above deficiencies. For a variety of linear regularization schemes as well as for conjugate gradient iteration it is shown to yield order optimal a priori error bounds under general smoothness assumptions. A posteriori error control is also possible, however at a sub-optimal rate, in general. This study uses and complements previous results for bounded deterministic noise.
| Author details: | Gilles BlanchardGND, Peter Mathe |
|---|---|
| DOI: | https://doi.org/10.1088/0266-5611/28/11/115011 |
| ISSN: | 0266-5611 |
| Title of parent work (English): | Inverse problems : an international journal of inverse problems, inverse methods and computerised inversion of data |
| Publisher: | IOP Publ. Ltd. |
| Place of publishing: | Bristol |
| Publication type: | Article |
| Language: | English |
| Year of first publication: | 2012 |
| Publication year: | 2012 |
| Release date: | 2017/03/26 |
| Volume: | 28 |
| Issue: | 11 |
| Number of pages: | 23 |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| Peer review: | Referiert |
